Contributions to Statistics
Bortkiewicz worked on mathematical statistics and its applications especially to actuarial science. There the focus of his work was on mortality tables. Examining life expectancy in a growing population he showed that contrary to received opinion life expectancy was not a function of the observed birth and death rates, but could only be computed from mortality tables.
He published several articles on the issue (see Bortkiewicz 1903, 1904, 1911; see also Samuelson 1976). He also applied his statistical methods to such diverse fields as radioactivity, order statistics, and legal studies.It has been argued that it would be more appropriate to call the Poisson distribution the Bortkiewicz distribution, because it had been established for the first time in a book entitled Das Gesetz der kleinen Zahlen (The Law of Small Numbers) published in 1898. In it Bortkiewicz studied events with a low frequency in a large population and showed that these followed a Poisson distribution even when the probabilities of the events varied. The case he had investigated was the number of soldiers annually killed by horse kicks per Prussian army corps. The observation period encompassed 20 years and he examined 14 corps. While the risk of lethal horse kicks varied across time and corps, a Poisson distribution fitted the overall distribution surprisingly well (Gumbel 1968).
Bortkiewicz was critical of Karl Pearson’s approach to statistics. He claimed that Pearson’s formulas designed to match observed results lacked a theoretical underpinning and were thus of no value. John Maynard Keynes in the Treatise on Probability (1921), while praising Bortkiewicz’s mathematical brilliance, questioned the meaning of his respective argument and maintained that it remained unclear what it really amounted to. Bortkiewicz’s approach to mathematical statistics did not gain general acceptance.